The partially observable Markov decision process (POMDP) provides a principled general framework for planning under uncertainty, but solving POMDPs optimally is computationally intractable, due to the "curse of dimensionality" and the "curse of history". To overcome these challenges, we introduce the Determinized Sparse Partially Observable Tree (DESPOT), a sparse approximation of the standard belief tree, for online planning under uncertainty. A DESPOT focuses online planning on a set of randomly sampled scenarios and compactly captures the "execution" of all policies under these scenarios. We show that the best policy obtained from a DESPOT is near-optimal, with a regret bound that depends on the representation size of the optimal policy. Leveraging this result, we give an anytime online planning algorithm, which searches a DESPOT for a policy that optimizes a regularized objective function. Regularization balances the estimated value of a policy under the sampled scenarios and the policy size, thus avoiding overfitting. The algorithm demonstrates strong experimental results, compared with some of the best online POMDP algorithms available. It has also been incorporated into an autonomous driving system for real-time vehicle control. The source code for the algorithm is available online.

POMDPs provide a principled framework for planning under uncertainty, but are computationally intractable, due to the “curse of dimensionality” and the “curse of history”. This paper presents an online lookahead search algorithm that alleviates these difficulties by limiting the search to a set of sampled scenarios. The execution of all policies on the sampled scenarios is summarized using a Determinized Sparse Partially Observable Tree (DESPOT), which is a sparsely sampled belief tree. Our algorithm, named Regularized DESPOT (R-DESPOT), searches the DESPOT for a policy that optimally balances the size of the policy and the accuracy on its value estimate obtained through sampling. We give an output-sensitive performance bound for all policies derived from the DESPOT, and show that R-DESPOT works well if a small optimal policy exists. We also give an anytime approximation to R-DESPOT. Experiments show strong results, compared with two of the fastest online POMDP algorithms.